Domains and Domain Walls in Multiferroic Ferroelectric-Ferromagnet and Control of Its Modulation

Ferroelectric-ferromagnet with inhomogeneous exchange-relativistic magneto-electric interaction (Dzyaloshinskii-Moriya) is studied theoretically in external electric field. The domain wall combines properties of usual 180 degrees. one in ferroelectric and unusual magnetic one, consisting of linear topological defects (Bloch lines), situated periodically with large density. It is shown that the external electric field changes both ferroelectric and ferromagnetic subsystems. It is found that the helicoids step is formed in each domain in the magnetic subsystem and Bloch lines period demonstrates incommensurate structure. Final solution for magnetic moment in Bloch lines and modulated helicoids period near domain wall can be expressed in Jacobian elliptic functions.